Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 117, 28 pages      arXiv:0712.1107      https://doi.org/10.3842/SIGMA.2007.117
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Self-Localized Quasi-Particle Excitation in Quantum Electrodynamics and Its Physical Interpretation

Ilya D. Feranchuk and Sergey I. Feranchuk
Department of Physics, Belarusian University, 4 Nezavisimosti Ave., 220030, Minsk, Belarus

Received October 21, 2007, in final form November 29, 2007; Published online December 07, 2007

Abstract
The self-localized quasi-particle excitation of the electron-positron field (EPF) is found for the first time in the framework of a standard form of the quantum electrodynamics. This state is interpreted as the ''physical'' electron (positron) and it allows one to solve the following problems: i) to express the ''primary'' charge e0 and the mass m0 of the ''bare'' electron in terms of the observed values of e and m of the ''physical'' electron without any infinite parameters and by essentially nonperturbative way; ii) to consider μ-meson as another self-localized EPF state and to estimate the ratio mμ/m; iii) to prove that the self-localized state is Lorentz-invariant and its energy spectrum corresponds to the relativistic free particle with the observed mass m; iv) to show that the expansion in a power of the observed charge e << 1 corresponds to the strong coupling expansion in a power of the ''primary'' charge e-10 ~ e when the interaction between the ``physical'' electron and the transverse electromagnetic field is considered by means of the perturbation theory and all terms of this series are free from the ultraviolet divergence.

Key words: renormalization; Dirac electron-positron vacuum; nonperturbative theory.

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